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C32×C11×Dic65 #38787993

order25740
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×Dic65

Splittings

derived, HallC5×C13 ⋊ C32×C4×C11
HallC32×C5×C11×C13 ⋊ C4
HallC32×C11×C13 ⋊ Dic5
HallC5×C11×C13 ⋊ C32×C4
HallC32×C5×C13 ⋊ C4×C11
HallC32×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ C32×Dic5
HallC32×C13 ⋊ C11×Dic5
HallC5×C11 ⋊ C32×Dic13
HallC32×C5 ⋊ C11×Dic13
SylowC13 ⋊ C32×C11×Dic5
SylowC5 ⋊ C32×C11×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11D65
commutator, hypocenterC5×C13C32×C4×C11
FrattiniC2C32×C11×D65
Fitting, socle, prime radicalC2×C32×C5×C11×C13C2
cosocleC2×C5×C13C2×C32×C11
LCSG ▷ C5×C13
UCSC1 ◁ C2×C32×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25740

Conjugacy classes & character table

6732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 224);